Category Error
by Qoheleth
Summary: Recalling a certain exploit of James T. Kirk's, Dr. Noonian Soong decides to put the new-made Data through a rather peculiar test.


Dr. Noonian Soong gazed lovingly upon his creation. After years of research, decades of labor, and a few more or less disastrous false dawns, he had at last achieved his dream: before him stood a man-made artifact whose intelligence and stability rivaled that of any natural humanoid. He imagined this was how Pythagoras had felt, when he had finally proved his famous theorem; perhaps he would have to sacrifice a hundred oxen of his own, when he revealed his achievement to the rest of Omicron Theta tomorrow.

Before he did that, though, there was one more test he needed to run. It was just possible that some wiseacre among his fellow colonists would recall James T. Kirk's legendary run-in with another wholly logical android, and try to find out if this one was vulnerable in the same way as that one had been. He needed to make sure of that point himself before he took the boy out in public; the last thing he needed was for his _magnum opus_ to go up in smoke at his first public appearance.

'Data?' he said.

'Yes, Father?' Data replied.

And Dr. Soong enunciated carefully, 'I am lying.'

* * *

'About what, Father?' said Data equably.

'About this,' said Dr. Soong. 'The statement that I'm making, right now – it's a lie.'

Data frowned, and considered this. 'I see,' he said. 'And what statement is that, exactly?'

Dr. Soong sighed; perhaps he hadn't made such an intelligent artifact, after all. 'I am lying,' he repeated patiently. 'That is the statement.'

'Ah,' said Data. 'Then what you are asserting, Father, is that the statement, "This statement is false," is false.'

Dr. Soong thought for a moment, and then nodded. 'Yes,' he said. 'That's exactly right, Data.'

'But then,' Data continued reflectively, 'by "this statement", you mean the statement that "This statement is false" is false. So what you really mean is, "The statement, '"The statement, ""This statement is false,"" is"'" … no, not that either. It would have to be, "The statement, '"The statement, ""The statement, '""This statement is""'"'" … no…'

He paused, and cogitated for a long moment, while his maker watched him attentively (and bootlessly) for any sign of smoke coming out of his ears. 'Father,' he said at length, 'there seems to be some error here. What you have made is not any kind of assertion at all, but rather a sort of infinite syntactic loop that can never arrive at its content. And if it is not an assertion, and it has no content, then it cannot very well be false – or true, either.'

Dr. Soong exulted inwardly. _Take that, Mudd,_ he thought.

* * *

Outwardly, however, he remained stern. There was still one loophole that Data's answer had left open; before he went about crying _Eureka!_ to Omicron Theta, he had to make sure that loophole was plugged, as well.

'So, then,' he said, 'you agree that I was lying, Data?'

'No, of course not,' said Data. 'Was I not clear? What you said had no content, and therefore was neither true nor false. So of course you were not lying, any more than you were telling the truth.'

'Ah,' said Dr. Soong, 'but if the statement wasn't false, then it was false to say that it _was_ false, wasn't it? So when I said that the statement, "This statement is false," was false, I must have been lying – and also telling the truth, since I was also saying that it was false to say that _that_ statement was false.'

Data fell silent, at that, for a full minute. 'Yes,' he said slowly. 'In a sense, Father, that is true. That is, if you were to say, "It is false to say that the syntactic loop denoted by the words, '"This statement is false,"' is false," then what you said would be true. But to impose that meaning on the loop itself, simply because it can be made to take something resembling that form, strikes me as an improper proceeding. So long as you remain within the loop, you must treat it, not as a loop, but as a real statement; thus, you can never arrive at the truth or falsity regarding it, because you are implicitly predicating things of it that its true nature will not bear. It would be like a man trying to find the prime factors of a rock; he would not be strictly wrong, since the rock does have a numerical aspect, but he will never find the truth he seeks so long as he confuses the rock itself with its number.'

At that, Dr. Soong permitted himself to beam with unalloyed pride upon his creation. 'Good lad, Data,' he said. 'I think you're ready for prime time.'

* * *

 **Disclaimer:** The statement, 'The statement, "It is false that Qoheleth owns _Star Trek_ ," is false,' is false.


End file.
